Graphics Reference
In-Depth Information
however because these reflections come out too sharp. This does not happen in real
life where things are fuzzier. Ray tracing captures the specular interaction between
objects very well but not the diffuse interactions. Radiosity methods deal with the
latter.
9.4.4
Radiosity Methods
First implemented in 1984 at Cornell University ([GoTG84]), radiosity methods are
view-independent solutions that are based on the conservation of light in a closed
world. The term
radiosity
, derived from the literature on heat transfer, refers to the
rate at which energy leaves a surface and is the sum of the rates at which energy is
emitted, reflected, or transmitted from that surface to others. We shall give more
details in the next chapter. Suffice it to say that the method is more complex than ray
tracing but it produces more realistic pictures even though it does not handle specu-
lar light correctly. It is possible to combine ray tracing and the radiosity approach.
9.5
The Rendering Equation
Looking back over what has been covered with regard to illumination in this chapter,
we see lots of different formulas and approaches. Kajiya ([Kaji86]) attempted to unify
the general illumination problem by expressing it in terms of finding a solution to a
single equation that he called
the rendering equation
:
È
Í
˘
˙
(
)
=
(
)
(
)
+
Ú
(
) (
)
I
pp
,
¢
g
pp
,
¢
e
pp
,
¢
r
pp p
,
¢ ≤
,
I
p p
¢ ≤
,
d
p
≤
,
(9.12)
surfaces
where
p
and
p
¢ are any two surface points,
I(
p
,
p
¢) is the intensity of light passing from
p
to
p
¢,
g(
p
,
p
¢) is a visibility term (which is 0 if
p
and
p
¢ cannot see each other and
inversely proportional to the square of the distance between the points
otherwise),
e(
p
,
p
¢) is the intensity of light emitted from
p
¢ to
p
,
r(
p
,
p
¢,
p
≤) is related to the intensity of all light reflected towards
p
from a point
p
¢ having arrived at
p
¢ from the direction to
p
≤, and
the integration is over all surfaces in the scene.
Notice that (9.12) is a recursive equation because the function I appears on both sides
of the equation. Also, each wavelength has its own equation (9.12). It can be shown
([WatW92]) that most of the illumination models discussed in this chapter are approx-
imations to the rendering equation. The rendering equation does not model every-
thing however. For example, it ignores diffraction and transparency.
